Abstract
We give generators for a certain complex hyperbolic braid group. That is, we remove a hyperplane arrangement from complex hyperbolic –space, take the quotient of the remaining space by a discrete group, and find generators for the orbifold fundamental group of the quotient space. These generators have the most natural form: loops corresponding to the hyperplanes which come nearest the basepoint. Our results support the conjecture that motivated this study, the “monstrous proposal”, which posits a relationship between this braid group and the monster finite simple group.
Citation
Daniel Allcock. Tathagata Basak. "Generators for a complex hyperbolic braid group." Geom. Topol. 22 (6) 3435 - 3500, 2018. https://doi.org/10.2140/gt.2018.22.3435
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